Node Elimination Technique

Node Elimination Technique:

Node Elimination Technique – In stability studies, it has been indicated that the buses to be considered are those which are excited by the internal machine voltages (transient emf s) and not the load buses which are excited by the terminal voltages of the generators. Therefore, in YBUS formulation for the stability study, the load buses must be eliminated. Three methods are available for bus elimination. These are illustrated by the simple system of Fig. 12.7(a) whose reactance diagram is drawn in Fig. 12.7(b). In this simple situation, bus 3 gets easily eliminated by parallel combination of the lines. Thus

Node Elimination Technique

Node Elimination Technique

Node Elimination Technique

Consider now a more complicated case wherein a 3-phase fault occurs at the midpoint of one of the lines in which case the reactance diagram becomes that of Fig. 12.8 (a).

Star-Delta Conversion

Converting the star at the bus 3 to delta, the network transforms to that of Fig. 12.8(b) wherein

Node Elimination Technique

Node Elimination Technique

Node Elimination Technique

Node Elimination Technique

This method for a complex network, however, cannot be mechainzed for preparing a computer programme.

Thevenin’s Equivalent

With reference to Fig. 12.8(a), the Thevenin’s equivalent for the network portion to the left of terminals a b as drawn in Fig. 12.8(c) wherein bus 1 has been modified to 1′.

Node Elimination Technique

Now

Node Elimination Technique

This method obviously is cumbersome to apply for a network of even small complexity and cannot be computerized.

Node Elimination Technique

Formulate the bus admittances for the 3-bus system of Fig. 12.8(a). This network is redrawn in Fig. 12.9 wherein instead of reactance branch, admittances are shown. For this network,

Node Elimination Technique

Node Elimination Technique

The bus 3 is to be eliminated.

In general for a 3-bus system

Node Elimination Technique

Since no source is connected at the bus 3

Node Elimination Technique

substituting this value of V3 in the remaining two equations of Eq. (12.31), thereby eliminating V3,

Node Elimination Technique

In compact form

Node Elimination Technique

Where

Node Elimination Technique

In general, in eliminating node n

Node Elimination Technique

Applying Eq. (12.34) to the example in hand

Node Elimination Technique

It then follows that

Node Elimination Technique

 

 

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